What do speaker judgments tell us about theories of quantifier scope in German ?

In this paper we use German data to evaluate configurational and multi-factor approaches to quantifier scope. Configurational theories derive scope relations syntactically at the level of Logical Form; semantic and pragmatic factors are either built into the syntactic representation or ignored, at least during the first derivational step. By contrast, multi-factor approaches consider syntactic, semantic and pragmatic properties of quantifiers as multiple constraints affecting quantifier scope. We examined predictions for quantifier scope in German of the configurational theory by Frey (1993) and of the multi-factor account by Pafel (2005). These fundamentally different approaches were tested in a series of picture verification experiments to assess scope preferences in doubly quantified German sentences. The results show that at least three factors affect the preferred scope. Our findings are neither fully consistent with Frey’s configurational theory nor with Pafel’s multi-factor approach; both theories made incorrect predictions for German doubly quantified sentences with a subject-before-object word order. For object-before-subject sentences, however, the experimental data by and large support the predictions of Pafel’s (2005) multi-factor approach.


Introduction
Intuitive judgments are the main data source semanticists rely on to formulate their theories.Often, however, semantic judgments are not very clear and preferences are gradientratherthanclear-cutandcategorical.Inparticular,scopeambiguityof quantifiers is a phenomenon where intuitions tend to be shaky.
The factors have been captured in different ways in different types of theoretical approaches.Inthispaperwecontrastsyntacticapproachestoquantifierscopewithmultifactor theories.The latter take into account syntactic as well as non-syntactic factors without drawing any qualitative distinctions between them.We will completely ignore semanticandpragmaticapproachestotheresolutionofquantifierscopeambiguity(see amongothersHendriks1993;Barker2002).Evenwiththislimitationinmindwecannot do justice to all existing scope theories but will focus on a very limited set of propos-alsdealingwithquantifierscopeinGerman(forgeneralreviewsseeKiss2006;Ruys& Winter2010;Szabolcsi2010;andSteedman2011).
Letusnowturntosentenceswithobject-before-subjectwordorder.Asshownabove, thissyntacticconfigurationopensupthepossibilityofinversescope.Thisdoesnotmean, however, that all sentences of this type should be fully ambiguous.Other, non-syntactic factorsmaystillinfluencescopepreferences.Wecanthinkofthemasfiltersonthesetof possiblereadingsthataregrammaticallylicensedinagivenconfiguration.Inprinciple,it may even be the case that one of the syntactically licensed readings is completely ruled out by some other factor or a combination of factors.
Indeed, it has been observed that quantifying expressions are not uniform with respect totheirtendencytotakewidescope(Szabolcsi2010),comparee.g.each and every vs. all.Someconfigurationalaccountshavedirectlybuiltinfluencesofprimafacienon-syntactic factorsintotheirrepresentations.Forinstance,Beghelli&Stowell(1997)havedeveloped a minimalist version of QR in terms of feature checking.Quantifiers take scope from different positions in a split-CP structure.In their theory distributive phrases like each boy have to check their features at LF at a projection DistP high up in the tree, while non-distributive phrases like all boysmayremainlow.Thisaccountsfortheinfluenceof distributivityonaquantifier'stendencytotakewidescope.Whatatfirstsightseemtobe lexicalsemanticdistinctionsbetweendifferentdeterminersarethusclaimedtobeconfigurationaldifferencesbetweenlogicalforms.Inprinciplethisstrategycanbeappliedto manyfactorsthataffectthescopalbehaviorofquantifyingexpressions.
An anonymous reviewer pointed out that the just given characterization of configurationalaccountsdoesnotdojusticetoagreatnumberofconfigurationaltheoriesthat have been proposed.Often syntactic interpretation is thought of as generating all combinatoriallypossiblescopereadingswithinagivensyntacticdomain.Someofthesereadingsmaysubsequentlybefilteredoutbyotherfactorssuchasderivationaleconomyin combination with logical entailments, plausibility, information structure, and so forth.Oncloserscrutinyconfigurationalaccountsshouldthereforebealsothoughtofasmultifactor theories.The experimental results reported below are admittedly fully consistent with such a view.However, the point just made may apply to such conceptions of relative scopeaswelldependingonhowthefilteringmechanismisspelledout.If,forinstance, lexicalpropertiessuchasthedistributivityofaquantifierfilteroutcertainreadingsbefore discoursepropertiesareconsidered,wewouldstillexpecttofindasymmetricaldependencies between scope factors.Thus, an important question is whether constraining factors are applied in parallel or in a strictly serial fashion.The results reported below indicate that the factors tested in the present paper work in parallel because they symmetrically contribute to the available readings.Our data therefore still have important implications for the architecture of the grammar.
To illustrate how scope preferences are derived under a multi-factor approach, we come back to the examples (2a) and (2b) from above.The following predictions are derived from Pafel's (2005) account of relative scope in German with one slight modification.Pafel uses threshold values, i.e. difference scores between quantifiers' "scope potentials", to distinguish between ambiguous and unambiguous sentences.We do not employ thresholds here because existing experimental work suggests that their use leads to a loss of explained variance relative to a model without thresholds (Bott & Radó 2007) Thefirsttwoquestionswillbeaddressedinourfirstexperiment(section3),whichisan explicitcomparisonofFrey'sandPafel'stheory.Thethirdquestionconcernsconfigurationalandmulti-factortheoriesingeneralandwillbetakenupinExperiments2and3 (section 4).Before going into the experimental study, we will first relate our research questions to existing psycholinguistic literature on quantifier scope ambiguity, then in section2wewilldiscussmethodologicalconsiderationsimportantforassessingquantifier scope preferences.
If the singular continuation were only compatible with a wide scope existential reading then the discourse in ( 9) should be incoherent, as this reading is excluded in the first sentence.The discourse is coherent, though, showing that the singular continuation does notfulfillitsfunctionofprovidingdisambiguation.Thiscouldresultinanoverestimation ofthe∃∀readings.Moregenerally,themethodusedtoassesswhetheraparticularreading is available must not introduce a distorting bias.In the experiments presented here, wewillthereforeuseapictureverificationtaskthathasbeenshowntoyieldreliableand validresults(Bott&Radó2007).Second, to evaluate the theoretical approaches outlined above we need to systematically investigate the interplay of the various factors that have received attention in the semanticliteratureonquantifierscope.Asoutlinedabove,acrucialtestofmulti-factor theoriesisexaminingtheirpredictionofpurelyadditivescopeinfluences.However,none of the existing psycholinguistic studies has manipulated multiple factors in tandem using the same participants, items and experimental procedure.
In their studies, however, distributivity was only manipulated across experiments.
Finally, almost all of these studies investigated quantifier scope in English.Because EnglishhasstrictSVOwordorder,inanactivedeclarativesentencethesubjectalways precedestheobject.Thustheeffectoflinearorder/c-commandrelationsandofthegrammatical function of the quantifiers cannot be readily distinguished.In other languages word order is much less constrained and these factors can be teased apart more easily.We thereforechoseGerman,wherethedirectobjectcanprecedethesubject.3This is illustratedin(10a)and(10b).( 10 However, there is one line of study that is closely related to the questions addressed in the presentpaper.Bott&Schlotterbeck(2012)examinedwhetherGerman object-before-subject and subject-before-object sentences both allow inverse scope readings.They were particularly interested in the readings that become available during the online interpretation ofdoublyquantifiedsentences.Theirstudyprovidedevidencethatsubject-before-object sentencesdifferfromobject-before-subjectsentencesinthatonlythelattergaveriseto online effects of scope ambiguity.The final interpretations as measured in an offline task,however,indicatedambiguityinbothtypesofconstructions.Furthermore,Bott& Schlotterbeck(2012)onlymanipulatedtheconfigurationthatthequantifiersappearedin, they did not investigate the interactions with other, non-syntactic scope factors.
Themodelontherightistrueonthe∃ =1 ∀ reading since there is exactly one student who was praised by all the teachers.It is false on the ∀∃ =1 reading because one student was praisedbymorethanoneteacher.Bycontrast,themodelontheleftistrueonthe∀∃ =1 reading because for each teacher there is exactly one student whom he praised.It is false onthe∃ =1 ∀ reading because there is no student who was praised by all the teachers.The ∃ =1 ∀diagramswerealwaysofthekindinFigure1(b),thatis,allofthemcontainedat least one additional line, which made the ∀∃ =1 reading false.
We are now able tooperationalize what shouldcount asscope preference (criterion to determine scope preference): Reading A is preferred over reading B if the A-disambiguationisratedbetterthantheB-disambiguation;iftheratingsareequal,the sentence is fully ambiguous. 5 In our experiments we used non-monotone exactly one in order to provide proper disambiguationsforthesentences(seee.g.themethodologicaldiscussioninRuys&Winter 2010).ThechoiceofquantifierwasalsocrucialfortestingFrey's(1993)theory,which only applies to a small number of quantificational expressions, namely those that are notambiguousbetweenspecific/referentialandquantificationalexpressions(i.e."indefinites")orbetweencollectiveandquantificationalexpressions(i.e."plurals").Thequantifiersgenau ein('exactlyone')andjeder ('every') Unfortunately,thetermambiguous is itself ambiguous.In the following we will distinguish between merely ambiguous, i.e. more than one interpretation is available regardless of whether one is preferred over the other, and fully ambiguous, i.e. the available interpretations are roughly equally preferred.Example (12a) employs a test used by Frey (1993).The sentence without exactly, i.e. indefiniteeine('a')allowsforaderereadingwherePeterbelievesthatheislovedby some woman without knowing that she is a vegetarian.This reading is not possible with exactly one,mirroringFrey'sobservationforthemonotonequantifiermindestens ein-('at least one').In other words, genau ein cannot take exceptional wide scope over believe.(12b)(cf.Fodor&Sag1982)showsthatexactly one cannot outscope the if-clause.The sentence only allows for the pragmatically marked interpretation that there is a strange inheritance rule according to which I inherit a fortune only if one but not more than one of my uncles dies (no matter which one).The specific interpretation, easily available without genau, becomes impossible once we add exactly. 6 The same goes for the unavailability of collective interpretations of jeder('every').Jeder cannot co-occur with collective predicates such as surround, form a line, or run apart resultinginoddinterpretationsin(13a)-(13c).Moreover,asmentionedaboveFreydismisses unmodifiedjeder and only uses fast jeder('almostevery').Thereasonisthatinhisview unmodifiedjeder makes reference to a given restrictor set, as evidenced by strong readings ofunmodifiedexamples (Dalrympleetal.1998;Schlotterbeck&Bott2013).Pafel(2005) almost every human/every human has a different smell 'Almosteveryhuman/Everyhumanhasadifferentsmell.' Thusthequantifiersjeder and genau ein,whichweusedtotestFrey'stheoryinExperiment 1(section3),satisfyFrey'sownrequirementsforbeingunambiguouslyquantificational.InExperiments2-3(section4)wewillalsocompareevery (one of these) with all (of these).The sole purpose of this comparison between jeder('every')andalle('all')istoexamine distributivityeffects;theresultsforconditionswithallewillnotbeusedtoevaluateFrey's theory but will only become relevant when testing the additivity of scope factors.

6
Ananonymousreviewersuggestedthatareferentialinterpretationmaybepossibleforexactly one in the following example with will('want')insteadofbelieve: (i) Peter will genau eine Vegetarierin heiraten.Peter wants exactly one vegetarian.femmarry 'Peterwantstomarryexactlyonevegetarian.' Our intuitions are the same as for believein(12a),buttheavailabilityofaspecificinterpretationforexactly one should be tested experimentally.We have to leave this to future research.

Materials
We constructed 36 doubly quantified sentences in three sentence conditions each (see AppendixAforthecompletelistofitems).Hereisasampleitem.
The so conditions provide evidence for the possibility of inverse scope in this constructiontype.Eventhoughthelinearinterpretationwasstronglypreferredovertheinverse reading(meanz-scores:0.This interaction was due to ambiguity in the ambiguous conditions as compared to the unambiguous controls.Finding ambiguity in this configuration of quantifiers provides primafacieevidenceagainstFrey's(1993)configurationalaccount.Inversescopereadingsseemtoexisteveninconstructionswherethesecondquantifierdoesnotc-command a trace of the first quantifier.Two paired t-tests were computed as follow-up analyses in order to break down the interaction.Interestingly, these analyses revealed that the ambiguityaffectedbothreadings.Itwasnotonlythecasethatsetdiagramsdisambiguating towards inverse scope were judged better in the ambiguous construction than in the disambiguatedcontrolcondition(t 1 (47)=5.29,p<.01;t 2 (35)=4.65,p<.01),but alsothereversewastrue:Setdiagramsonlyconsistentwiththestronglypreferredlinear interpretation were judged significantly worse in the ambiguous condition than in the appropriatecontrolcondition(t 1 (47)=-3.41,p<.01;t 2 (35)=-3.43,p<.01).
Comparingtherelativedifferencesbetweenthelinearandtheinversedisambiguation in the so and the os1conditionsweseethatPafel'spredictionsarenotmetintheso conditions.Under his theory we would have expected differences of the same size in both construction types.This was clearly not the case.While the linear and the inverse interpretation were more or less equally available in the ambiguous os1 conditions, the soconditionsshowedastrongpreferenceforlinearscope.So,couldFrey'saccountbeon therighttrackafterall?Asoutlinedintheintroduction,Freyacknowledgestheinfluence ofnon-syntacticfactorssuchaslexicalpropertiesofquantifiersandintonation.Wehave showninsection2thatthetestedquantifiersarequantificationalexpressionsaccording toFrey'scriteria.However,participantsmaysometimeshaveimplicitlychosenanintonation that made inverse scope available (see, e.g.Fodor 2002 for empirical evidence forimplicitprosodyduringsilentreading).Morespecifically, Krifka(1998),buildingon workbyBüring(1997),hasproposedthatarise-fallintonationcontourmightaddthe inverse reading, which is impossible otherwise.If this is correct, the ambiguity observed in the so conditions may be due to the fact that participants sometimes chose a rise-fall intonation contour in order to license inverse scope.Note that this could also explain thedifferencebetweenthefindingsofthepresentexperimentandBott&Schlotterbeck's (2012)resultswhodidnotfindanyevidenceforinversescopeinthesameconstruction when the sentences were presented in a self-paced fashion.It is plausible that in that kind of task readers are not able to construe the sentences with a rather marked rise-fall intonationcontour.Inanofflinetaskastheoneusedhere,however,choosingtheappropriate implicit prosody is probably much easier.We therefore ran a pilot study explicitly addressing the role of intonation for scope inversion in subject-before-object sentences.The experimentusedpictureverificationwithauditorypresentationofstimulicontrolledfor intonation.

The potential influence of intonation (Pilot study)
Weconstructed20itemsinfourconditionsaccordingtoa2×2(intonation×disambiguation) within design.Target sentences with the universal distributive subject quantifierjederprecedingtheobjectquantifiergenau ein('exactlyone')wereembedded inshortdialogues: 8 8 Ananonymousreviewerremarkedthattheinversescopeanswerin(18a)maybeexcludedonpragmatic grounds: It may simply be irrelevant how many pieces the children share.To us, the question itself is ambiguous allowing for an interpretation is it many black pieces that belong to both Andrea and Wolfgang?licensing an inverse scope construal of the answer.When designing the experiment, we decided against presenting decontextualised statements without a preceding question because naive informants might not be able to infer the underlying information structure.We agree that more careful testing is required.This iswhywewerehesitanttocallthispilotstudya"realexperiment".Futureworkisrequiredtoconfirmthe assumptions underlying the pilot study.between these intonation contours and stated afterwards that to her both were possible answers to the how manyquestionin(18b). 20nativeGermanparticipantsjudgedthe20itemsplus60fillerdialoguesinalatin squaredesignmakingsurethattheysaweachiteminonlyonecondition.Afterinspecting the picture and listening to the auditorily presented dialogue they had to judge whether theanswerofspeakerBwasatruedescriptionofthepicturebyprovidinga"yes,true" or"no,false"answer.
This provides preliminary evidence against the view that doubly quantified German sentences with a subject-before-object word order can receive an inverse scope interpretation,orreceiveitmoreeasily,ifrealizedwitharise-fallintonation.Comingbacktothe resultsofExperiment1wethusconcludethatitisunlikelythatparticipantsmadeinverse scopeavailablebyimplicitlyimposingarise-fallintonation.Wewouldliketoemphasize, though,thattheinfluenceofintonationonscopeinterpretationneedstobeinvestigated more carefully.We must leave this for future research.

Experimental materials
The constructions tested in Experiment 2 and 3 are presented in ( 19) and ( 20).The completelistofitemsisprovidedinAppendixB.
Materials and design:Weusedthe24doublyquantifiedtransitivesentencesinthefour variantsin( 19).Theuniversallyquantifiedphrasewasthesubjectandtheexistentially quantifiedanddiscourseanaphoricexactly one of these-quantifierwasthedirectobject.Each item was paired with two disambiguating set diagrams like the ones in Figure 1 resultingina2×2×2factorialdesignwiththewithinfactorslinearorder, distributivity and disambiguation.Additionally, we prepared 36 distractor sentences using differentquantifiers,negationanddefinitedescriptions.16fillersweretrueand20werefalse.We constructed eight lists according to a latin square design.
The experiment was a paper-and-pencil questionnaire.After reading written instructions,participantsfirstcompletedashortpracticesessionconsistingoffivetrials.Inthe following experimental session, sentence-picture pairs were presented in an individually randomizedorder.Eachsentence-picturepairwaspresentedonaseparatepageinasmall bookletwiththereferenceitemontopofeachpage(Many hunters have shot two rabbits inasituationinwhich4outof10huntersshottwoandtherestshotnone).Participants were explicitly instructed not to go back to earlier items and to complete the experiment in a page-by-page fashion.

Manipulating distributivity and discourse anaphoricity (Exp. 3)
Discourse anaphoricity of the restrictor set has not received very much attention in the literatureonquantifierscope.AnexceptionisMusolino&Gualmini( 2004),whoinvestigated inverse scope construals in children's understanding of sentences including negationandquantifierssuchas(21).Theyfoundthatdiscourseanaphoricquantifierssignificantlyincreasedchildren'sability to compute non-isomorphic, inverse interpretations, which were largely absent in sentences without the partitive.Here, we employed this factor to test whether and how discourse related scope factors interact with lexical factors such as distributivity.
Figure 9 shows the observed difference scores between the mean judgments for the linear disambiguation minus the mean judgments for the inverse disambiguation.The observeddifferencescoresareplottedagainstthedifferencescorespredictedbyPafel's (2005)theory.AsinExperiment2,thereisaratherclosecorrespondencebetweenthe actualscopejudgmentsandthevaluespredictedbythetheory.Again,thisisonlytruefor observedandpredictedvaluesafterz-transformation(cf.fn.9).Wehypothesizethatthe stronger-than-expected tendency for linear interpretations in the present experiment com-paredtothepreviousoneisduetoahigherproportionofOVSsentencesinExp.3.Note that a decrease in the factor weight for subjecthood leads to a stronger preference for linearscopeinOVSsentences.Weconsideritaninterestingquestionforfutureresearch to investigate how contextual factors such as the broader context of the experiment probabilisticallycontributetotherelativescopeofquantifiers.
The configurational theories we considered here disambiguate the relative scope of quantifying expressions in the syntax.In Frey's account inverse scope in German can onlyariseinconfigurationsinwhichthesecondquantifierhassyntacticcommandover a trace left in the base position of a quantifier in a fronted position.The results of Experiment 1 provide evidence against Frey's scope principle.Using quantificational expressions that satisfy Frey's constraints, inverse scope was more acceptable in the tested subject-before-object construction than in the unambiguous baseline control condition.Accordingtoourcriterionfordeterminingscopeambiguity,wethereforeconclude thatthefirstresearchquestionare German doubly quantified subject-before-object sentences scope unambiguous must be answered in the negative.This claim is further supported by our pilot study suggesting that inverse scope in this construction type cannot be explainedbyproposedprosodicinfluencesonquantifierscopeinGerman.Wewould alsoliketopointoutthatwefoundstrongdifferencesinscopepreferencesforsentences withfrontedobjectquantifiers.Asitstands,Frey'stheorydoesnotmakeanyspecific predictions for these except for the general claim that they should in principle allow for bothlinearandinversescopeconstruals.Forthesecases,theempiricalcoverageofthe theory is thus rather limited and something needs to be added to explain the observed differences.
Unconstrained versions of configurationalaccounts would predict all combinatorially possible scope readings to be available, at least in principle.This is in line with the present findings.Whatneedstobedoneistoworkoutanexplanativemodelofscopepreference incorporatingtheinterplayofthedifferentfactorshereshowntoberelevantfortherelativescopeofquantifiers.Furthermore,wehavearguedintheintroductionthatthepresenteddataposesomeconstraintsonsuchamodel,namelythatthefactorsthatfilterout particular scope readings have to contribute in parallel.We hope that the data presented here will serve as a valuable data source for working out such a model.
Thefindingsofourexperimentslendsomesupporttomulti-factortheoriesofquantifierscope.First,relativescopeisinfluencedbyanumberoffactorssuchaslinear order, distributivity and discourse anaphoricity.Second, scope preferences were graded rather than categorical and, at least for object-before-subject sentences, largely fit the predictions derived from the tested linear model of scope preference.Third,thefactorsinteractinapurelyadditivefashion.ContrarytoPafel's(2005)model, ourfindingsdonotsupporttheassumptionofthresholdsdistinguishingambiguousfrom unambiguoussentences.Alltheconstructionswetestedinourexperimentswerescope ambiguous.Experiment1makesthestrongestcaseforthisclaim.Althoughonescope reading was extremely preferred over the other, the dispreferred interpretation was still judgedbetterthanaclearlyunavailableoneinscopedisambiguatedcontrols.Moreover, theratingsofcanonicalsubject-before-objectsentencesinExperiment1indicatedthat Pafel's (2005) account makes the wrong predictions for this kind of sentences.Here, thetheoryclearlyhastobeadjustedtofitthedata.Wehavealsoseenthatthebroader experimentalcontexthasaninfluenceonscopejudgments.Identicalconditionstested in Exp. 2 and 3 received consistently different judgments.This shows that we need additional linking assumptions to relate linguistic theory to experimental work on scope preferences.
Besides the theoretical implications, our study adds to the psycholinguistic work on quantifier interaction.Previous results were not sufficient to decide whether linear order has an influence above and beyond grammatical function.While VanLehn (1978), Fodor(1982), Gillen(1991),andKurtzman&MacDonald(1993)providedsupport in favor of this claim, Ioup (1975), Catlin &Micham (1975), andMicham et al. (1980)arguedthatthegrammaticalfunctionofthequantifiersismoreimportantthan linear order.The constructions we used made it possible to tease apart the two factors.Wefoundastrongeffectoflinearorderindicatingthattheorderofquantifiersinfluences scope independent of grammatical function.Furthermore, our study lends support to the findings of Tunstall (1998), Bott & Radó (2009), Radó &Bott (2012), andBrasovaeanu &Dotlacil (2015) in showing effects of distributivity.Finally, it adds discourseanaphoricity to the list of scope factors, which has not been investigated beforewithrespecttoscopepreferencesinadults(Syrettetal.2016)buthasbeendemonstrated to yield rather strong effects in children's interpretation of scope (Miller & Schmitt2004;Musolino&Gualmini2004).
Whatismore,ourstudyisoneofthefirstexperimentalinvestigationsonthecombined influenceofmultiplescopefactors.Wehavedemonstratedthatthefactorsclaimedtobe relevantforscopeinterpretationshowpurelyadditiveeffectsaspredictedbymulti-factor models that take into account the linear combinations of multiple constraints.In spite of being descriptively adequate, multi-factor theories are not very popular in the linguistic literature.Therearereasonsforthis.Sofar,thistypeoftheoryjuststatesthatafactor isrelevantforquantifierscopewithoutofferinganexplanationwhythisshouldbethe case.To also strive for explanatory adequacy, multi-factor theories need to address this question.
Participants'taskwastodecidewhetherB'sanswercorrespondsto  atruedescriptionofthescenario.SpeakerB'sanswerinthedialogue(18a)isaninformative answer to the question under both scope readings.In its linear scope construal the answer is that neither of the two children has many black pieces because each has only one(cf.Figure4(a)).Undertheinversescopeconstrual,theanswersaysthatthereisonly oneblackpiecethatAndreaandWolfganghaveintheirjointarea(cf.Figure4(b)),which again shouldn't count as an instance of many.Thedialogue(18b)servedasbaselinecontrol.Here, only the linear reading should be possible.Dialogues were spoken and recorded by a male (speaker A) and a female speaker (speaker B).Speaker B was instructed to produce the answer in the rise-fall dialogues (18a)witharise-fallintonation.Forthecontrolcondition(18b)speakerBwasaskedto use what seemed the most appropriate intonation for the answer given the question.The producedintonationcontoursofspeakerBwereanalyzedwithrespecttotheirfundamen-talfrequencyusingthePRAATsoftwarepackage(Boersma2001).Theaverageintonation contoursinthetwodialogueconditionsareshowninFigure5.Inthecontrolcondition abouthalfoftheitemswererealizedwithtwofocionthetwoquantifiersandtheother halfwithverumfocusontheauxiliary.Whilerecordingthestimuli,speakerBchanged

Figure 5 :
Figure 5: Intonation contours of the target sentences in the pilot study: (a) Mean F0-contour rise-fall used for dialogues of type (18a); (b) Mean F0-contour rise-fall used for dialogues of type (18b).Plots show mean F0-values split by sentence regions and 95% confidence intervals.

Figure 7 :
Figure 7: Observed and predicted difference scores in Experiment 2. Both observed and predicted mean difference scores in the four sentence conditions were normalized via z-transformations for better comparability.

Figure 9 :
Figure 9: Observed and predicted difference scores in Experiment 3.Both observed and predicted mean difference scores in the four sentence conditions were normalized via z-transformations for better comparability.
, however, observes that basically the same readings are available for jeder and fast jeder in(13d).Themostnaturalinterpretationforthesentenceisthatfor(almost)eachpairof individualsfromthedomainthetwoindividualsdifferintheirsmell.Thisinterpretation is available with or without almost,contrarytoFrey'sproposal.Inordertoavoidproblems due to the inherent vagueness of almostwethereforeusedunmodifiedjeder in the experiments reported below.
Fürgenau einen Lehrer gilt: Er lobte jeden dieser Schüler.for exactly one teacher holds:He.nompraised each these pupils.acc'Exactlyoneteacherissuchthathepraisedeachofthesepupils.' Eachofthesixsentenceconditionswaspairedwithapicturethatwasonlycompatible with the ∀∃ =1 orthe∃ =1 ∀ reading.This yielded a total of twelve sentence-picture pair 7Totestthispredictionweaddedthreescopeunambiguouscontrolswithquantifiers appearing in clause bounded position.If the potentially ambiguous subject-before-object construction (15c) should turn out to be indistinguishable from a corresponding scope unambiguouscontrolconditionwecanlegitimatelytakeittobeunambiguous.Consider thesampleiteminthethreecontrolconditionsin(17).